"These people are cowards. They're not going to walk into a school if 20% of the teachers have guns -- it may be 10% or may be 40%. And what I'd recommend doing is the people that do carry, we give them a bonus. We give them a little bit of a bonus," Trump said. "They'll frankly feel more comfortable having the gun anyway. But you give them a little bit of a bonus."

White House Principal Deputy Press Secretary Raj Shah told reporters after Trump's comments that the proposal hasn't reached the policy or legislative point yet, but downplayed questions about how the plan would be funded.

"I think that if we find the policy solutions that make the most sense that we can get buy in for, we'll figure out the rest of the pieces that you outlined," he said.

Asked about the cost of a plan -- which could be well into the hundreds of millions of dollars -- Shah again repeated that the policy "hasn't been fleshed out" but added, "Do we really think that that's too much to pay for school safety?"

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Trump proposed a series of measures to respond to the shooting in Parkland, Florida, during a freewheeling session at the White House.

Randi Weingarten, head of the American Federation of Teachers, knocked the proposal in a statement on behalf of the teachers' union.

"Teachers don't want to be armed," Weingarten said. "We want to teach. We don't want to be, and would never have the expertise needed to be, sharp shooters; no amount of training can prepare an armed teacher to go up against an AR-15."

At the session, Trump repeated his suggestion that some teachers get trained to handle firearms as a deterrent to shooters and disparaged "gun-free zones."

"I don't want teachers to have guns. I want certain highly adept people -- people that understand weaponry, guns. If they really have that aptitude -- because not everybody has aptitude for gun -- but if they have the aptitude, I think a concealed permit for having teachers and letting people know that there are people in the building with guns, you won't have -- in my opinion -- you won't have these shootings," the President said.

Gun-free zones, meanwhile, are appealing to criminals, he said.

"We have to harden those schools, not soften them. A gun-free zone, to a killer, or somebody that wants to be a killer, that's like going in for the ice cream. That's like saying, 'Here I am, take me,' " Trump said at the White House.

"They see that as such a beautiful target," Trump said. "They live for gun-free zones."

He also disparaged school shooting drills, saying they were tough on the kids.

"Active shooter drills is a very negative thing, I'll be honest with you," he said. "I think that's a very negative thing to be talking about. I don't like it. I don't want to tell my son 'you're going to have to participate in an active shooter drill. I'd much rather have a hardened school."

Trump also promoted the idea of increasing the age limit of those who can purchase semi-automatic rifles from age 18 to age 21 as well as looking at the possibility of committing people like the Florida shooter to mental institutions.

"I said this yesterday when we had a mental institution where you take a sicko like this guy -- he was a sick guy, so many signs -- and you bring him to a mental health institution, those institutions are largely closed because communities didn't want him," Trump said.

The President also blamed violence in video games and movies as partly responsible for shaping young people's thoughts.

"They're so violent," Trump said.

Trump told the roundtable that he has spoken to officials from the National Rifle Association, calling them "good people" and "patriots" who are "ready to do things."

"They're ready to do things. They want to do things. They are good people. They are patriots. They love this country," he said. "The NRA is ready to do things. People like to blame them, and they do have power and all of that, but they want to do things."

"I told them, 'We're going to have to toughen up. It doesn't make anyone look good. We can't allow that to happen,'" Trump said.